Locally distinguish unextendible product bases by efficiently using entanglement resource

Abstract

Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone, can always be locally distinguished using quantum teleportation with enough entanglement resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following open question: how to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement resource. In this paper, we first present two protocols to locally distinguish a set of unextendible product bases (UPB) in $5\otimes 5$ by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in $d\otimes d$, where $d$ is odd and $d⩾3$. Furthermore, for a class of UPB in $d\otimes d$, where $d$ is even and $d⩾4$, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently, and also reveal the phenomenon of less nonlocality with more entanglement.

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Cited by in corpus (9)

• Strong quantum nonlocality with entanglement
• Strongly nonlocal unextendible product bases do exist
• Multiparty orthogonal product states with minimal genuine nonlocality
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Strong quantum nonlocality from hypercubes